Last visit was: 17 Oct 2026, 21:44 It is currently 17 Oct 2026, 21:44
Decision Tracker
My Rewards
New comers' posts
New posts
Unanswered

Close

GRE Prep Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GRE score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Go to My Error Log Learn more
Close

Request Expert Reply

Confirm Cancel
PREVIOUS TOPIC
NEXT TOPIC

(x^y) * (x^2)=x^6

Tags :
Find Similar Topics  About  Add a Tag

Show Tags
Hide Tags

User avatar
D
Carcass
Verbal Expert
Joined: 18 Apr 2015
Posts: 36321
Own Kudos [?]: 43642 [16]
Given Kudos: 27315
Send PM
(x^y) * (x^2)=x^6 [#permalink] New post   29 Jun 2020, 08:33
2
Expert Reply
14
Bookmarks
00:00

Question Stats:

43% (01:09) correct 56% (00:57) wrong based on 309 sessions

Hide Show timer Statistics

\((x^y) \times (x^2)=x^6\) and \((2z)^{-2} = \frac{1}{36}\)

Quantity A
Quantity B
\(\frac{1}{y}\)
\(\frac{1}{z}\)



A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
ShowHide Answer
Official Answer
D
Most Helpful Community Reply
User avatar
P
GreenlightTestPrep
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Own Kudos [?]: 12851 [9]
Given Kudos: 136
Send PM

Top Member of the Month
Re: (x^y) * (x^2)=x^6 [#permalink] New post   30 Jun 2020, 13:14
6
3
Bookmarks
Carcass wrote:
\((x^y) \times (x^2)=x^6\) and \((2z)^{-2} = \frac{1}{36}\)

Quantity A
Quantity B
\(\frac{1}{y}\)
\(\frac{1}{z}\)




There are lots of problems with this question

Given: \((2z)^{-2} = \frac{1}{36}\)

Rewrite as: \(\frac{1}{(2z)^2} = \frac{1}{36}\)

Simplify: \(\frac{1}{4z^2} = \frac{1}{36}\)

From this we can conclude that: \(4z^2 = 36\)

Divide both sides by 4 to get: \(z^2 = 9\)

So, z = 3 OR z = -3


Given: \((x^y) \times (x^2)=x^6\)
One possible solution here is: x = 5 and y = 4, since (5^4)(5^2) = 5^6
Another possible solution is: x = 0 and y = 99, since (0^99)(0^2) = 0^6
Another possible solution is: x = 1 and y = -7, since (1^77)(1^2) = 1^6
.
.
.etc

Since y can have infinitely many values, the correct answer here is D

Cheers,
Brent
General Discussion
User avatar
D
Carcass
Verbal Expert
Joined: 18 Apr 2015
Posts: 36321
Own Kudos [?]: 43642 [0]
Given Kudos: 27315
Send PM
Re: (x^y) * (x^2)=x^6 [#permalink] New post   29 Jun 2020, 08:33
Expert Reply
Post A Detailed Correct Solution For The Above Questions And Get A Kudos.
Question From Our New Project: GRE Quant Challenge Questions Daily - NEW EDITION!
avatar
dpokushalov
Intern
Intern
Joined: 23 Jun 2020
Posts: 30
Own Kudos [?]: 42 [2]
Given Kudos: 0
Send PM
Re: (x^y) * (x^2)=x^6 [#permalink] New post   29 Jun 2020, 10:26
2
So first we know that (x^y) * (x^2) = x^6
When we multiply two numbers that are expressed as x raised to some power, the result is x raised to the power of the sum of the two powers
So in our case 6 = y+2 which means y=4

Next:
(2z)^−2= 1/36

(2z)^-2 = 1/(2z)^2 = 1/(4z^2)

Now since 1/(4z^2) = 1/36 , we calculate z = 3

Lastly, we just compare 1/3 to 1/4 resulting in B as the right answer
User avatar
D
Carcass
Verbal Expert
Joined: 18 Apr 2015
Posts: 36321
Own Kudos [?]: 43642 [0]
Given Kudos: 27315
Send PM
Re: (x^y) * (x^2)=x^6 [#permalink] New post   29 Jun 2020, 10:29
Expert Reply
\((x^y) \times (x^2)=x^6\)

\(x^{y+2}=x^6\)

\(y=4\)

\((2z)^{-2} = \frac{1}{36}\)

\(\frac{1}{(2z)^2}=\frac{1}{36 }\)

\(\frac{1}{2^2 \times z^2}=6^2\)

Basically

\(4z^2=36\)

\(z^2=9\)

\(z=3\)

So y=4 and z=3

A is \(\frac{1}{4}\) and B is \(\frac{1}{3}\)

B is greater
avatar
tpaillier
Intern
Intern
Joined: 23 Jan 2020
Posts: 18
Own Kudos [?]: 31 [0]
Given Kudos: 0
Send PM
Re: (x^y) * (x^2)=x^6 [#permalink] New post   30 Jun 2020, 08:45
Carcass wrote:
\((x^y) \times (x^2)=x^6\)

\(x^{y+2}=x^6\)

\(y=4\)

\((2z)^{-2} = \frac{1}{36}\)

\(\frac{1}{(2z)^2}=\frac{1}{36 }\)

\(\frac{1}{2^2 \times z^2}=6^2\)

Basically

\(4z^2=36\)

\(z^2=9\)

\(z=3\)

So y=4 and z=3

A is \(\frac{1}{4}\) and B is \(\frac{1}{3}\)

B is greater


Could help explain why can't z also be -3?
User avatar
D
Carcass
Verbal Expert
Joined: 18 Apr 2015
Posts: 36321
Own Kudos [?]: 43642 [0]
Given Kudos: 27315
Send PM
Re: (x^y) * (x^2)=x^6 [#permalink] New post   30 Jun 2020, 10:24
Expert Reply
Attachment:
shot122.jpg
shot122.jpg [ 257.46 KiB | Viewed 12856 times ]


We have created the Quant math book for this purpose.

https://gre.myprepclub.com/forum/greprepcl ... -2609.html

Use it :wink:
avatar
Unperturbable
Intern
Intern
Joined: 28 Jan 2020
Posts: 2
Own Kudos [?]: 3 [3]
Given Kudos: 0
Send PM
Re: (x^y) * (x^2)=x^6 [#permalink] New post   30 Jun 2020, 13:03
3
So, Z can be +3 or -3 right?
avatar
tpaillier
Intern
Intern
Joined: 23 Jan 2020
Posts: 18
Own Kudos [?]: 31 [2]
Given Kudos: 0
Send PM
Re: (x^y) * (x^2)=x^6 [#permalink] New post   Updated on: 30 Jun 2020, 13:15
2
Carcass wrote:
Attachment:
shot122.jpg


We have created the Quant math book for this purpose.

https://gre.myprepclub.com/forum/greprepcl ... -2609.html

Use it :wink:



I didn't know about this. Thanks a lot, it's very good.
But I am even more confused now, because as it says in this Quant book:

Carcass wrote:
This post is a part of [GRE MATH BOOK]


Exponential Equations:
When solving equations with even exponents, we must consider both positive and negative possibilities for the solutions.

For instance \(a^2=25\), the two possible solutions are \(5\) and \(-5\).


so in our example, z^2 = 9 ; z = 3 or - 3 ? right?
can you help shed some light here?

Originally posted by tpaillier on 30 Jun 2020, 13:14.
Last edited by tpaillier on 30 Jun 2020, 13:15, edited 1 time in total.
User avatar
D
Carcass
Verbal Expert
Joined: 18 Apr 2015
Posts: 36321
Own Kudos [?]: 43642 [0]
Given Kudos: 27315
Send PM
Re: (x^y) * (x^2)=x^6 [#permalink] New post   30 Jun 2020, 14:20
1
Expert Reply
Clear the way guys.

IF the variable is x^2= some value for instance x^2=25

x is equal to 5 AND minus 5

And the book is right. After all this is a universal math law.

Back to the question, I checked out the book from which I took it and YEs the book is wrong and @greenlighttest prep is RIGHT (as almost always) and the GRE Quant book I made is Correct . However, the book from the question comes from is WRONGG

\(z^2= 9\) ---------> z=+3 or -3

So in one case the answer is B and in the other case the answer is A

So the definite answer is D

Many Thanks
User avatar
bumpbot
GRE Prep Club Legend
GRE Prep Club Legend
Joined: 07 Jan 2021
Posts: 6090
Own Kudos [?]: 87 [0]
Given Kudos: 0
Send PM
Re: (x^y) * (x^2)=x^6 [#permalink] New post   14 Oct 2025, 02:11
Hello from the GRE Prep Club BumpBot!

Thanks to another GRE Prep Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
Prep Club for GRE Bot
gmatclubot
Re: (x^y) * (x^2)=x^6 [#permalink]
14 Oct 2025, 02:11
Moderators:
adewale223
GRE Instructor
167 posts
bronaugust
GRE Forum Moderator
37 posts
VibhuAnurag
GRE Instructor
275 posts
Nsp10
Moderator
45 posts
tyrant100
GRE Forum Moderator
144 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Main navigation

Partners

GRE Resources

www.ets.org/gre | About | Terms and Conditions and Privacy Policy | Prep Club for GRE Rules | Contact | Advertise